Abstract We study the minimization of a spectral functional made as sum first eigenvalue Dirichlet Laplacian and relative strength Riesz-type interaction functional. show that when Riesz repulsion is below critical value, existence minimizers occurs. Then we prove, by means an expansion analysis, ball rigid minimizer small enough. Eventually for certain regimes repulsion, regular do not exist.

While CaMKII has long been known to be essential for synaptic plasticity and learning, recent work points to new dimensions of CaMKII function in the nervous system, revealing that CaMKII also plays an important role in synaptic organization. Ca(2+)-triggered autophosphorylation of CaMKII not only provides molecular memory by prolonging CaMKII activity during long-term plasticity (LTP) and lear...